Bias of LS estimators in nonlinear regression models with constraints. Part II: Biadditive models

Denis, Jean-Baptiste, and Pázman, Andrej. "Bias of LS estimators in nonlinear regression models with constraints. Part II: Biadditive models." Applications of Mathematics 44.5 (1999): 375-403. <http://eudml.org/doc/32524>.

@article{Denis1999,
abstract = {General results giving approximate bias for nonlinear models with constrained parameters are applied to bilinear models in anova framework, called biadditive models. Known results on the information matrix and the asymptotic variance matrix of the parameters are summarized, and the Jacobians and Hessians of the response and of the constraints are derived. These intermediate results are the basis for any subsequent second order study of the model. Despite the large number of parameters involved, bias formulæ turn out to be quite simple due to the orthogonal structure of the model. In particular, the response estimators are shown to be approximately unbiased. Some simulations assess the validity of the approximations.},
author = {Denis, Jean-Baptiste, Pázman, Andrej},
journal = {Applications of Mathematics},
keywords = {asymptotic variance; bilinear model; nonlinear least squares; response function; second order approximation; asymptotic variance; bilinear model; nonlinear least squares; response function; second order approximation},
language = {eng},
number = {5},
pages = {375-403},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bias of LS estimators in nonlinear regression models with constraints. Part II: Biadditive models},
url = {http://eudml.org/doc/32524},
volume = {44},
year = {1999},
}

TY - JOUR
AU - Denis, Jean-Baptiste
AU - Pázman, Andrej
TI - Bias of LS estimators in nonlinear regression models with constraints. Part II: Biadditive models
JO - Applications of Mathematics
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 5
SP - 375
EP - 403
AB - General results giving approximate bias for nonlinear models with constrained parameters are applied to bilinear models in anova framework, called biadditive models. Known results on the information matrix and the asymptotic variance matrix of the parameters are summarized, and the Jacobians and Hessians of the response and of the constraints are derived. These intermediate results are the basis for any subsequent second order study of the model. Despite the large number of parameters involved, bias formulæ turn out to be quite simple due to the orthogonal structure of the model. In particular, the response estimators are shown to be approximately unbiased. Some simulations assess the validity of the approximations.
LA - eng
KW - asymptotic variance; bilinear model; nonlinear least squares; response function; second order approximation; asymptotic variance; bilinear model; nonlinear least squares; response function; second order approximation
UR - http://eudml.org/doc/32524
ER -